I don't really understand what you're trying to say.
I think there's two things going on in your comment: you want more information about emergent theories, and you want more information about how time emerges in a theory that is symmetrical under time reversal.
For the first, perhaps you should try Sabine Hossenfelder's video and video-transcript at <https://backreaction.blogspot.com/2020/04/what-is-emergence-...> first, rather than something more technical.
For the second: your paraphrasing, particularly "if you disagree your logic is broken" is in my view unfair to the quoted scientists and the author & editor. However here's a handful of paragraphs on how time can be understood as an emergent property.
tl;dr of below: the behaviour of matter in the bulk breaks the time-reversal symmetry of fundamental physical equations and provides a "clock" that solutions of these equations do not. Since a direction of time can't be obtained by these fundamental equations, but can be obtained by non-fundamental bulk behaviour theories (like statistical mechanics, which captures the collective behaviour of many items described by fundamental theories, with that collective behaviour being qualitatively different than individual behaviour) time can be said to be emergent.
I'm hoping that your "logic is broken" paraphrase is just that you don't understand that any monotonic function on a path through spacetime can serve as a clock, and while there is no a priori correct path, there is always at least one extreme path through spacetime from which one can take a global notion of time. For example, in the FLRW universe, the comoving coordinate time is suitable. However, this time is not the wristwatch time of an observer who sometimes accelerates to a significant fraction of c, and sometimes decelerates to a tiny fraction of c, and the function transforming the two times (comoving time and this particular proper time) is complicated.
Connes & Rovelli in the early 1990s originated the idea of using Boltzmann entropy as a "universal" clock comparable to comoving time: in both cases the behaviour of bulk matter allows for a set of coordinates that most observers can relate to their proper time. Entropy is more general since it's not restricted to an expanding and at large scales isotropic and homogeneous universe; it just requires thermodynamic matter. The details are in papers which are probably too technical for most -- a copy of their 1994 paper in Classical and Quantum Gravity can be found at <https://arxiv.org/abs/gr-qc/9406019>.
One could summarize: galaxy clusters spread apart with high-quality vacuum growing in between them; in galaxy clusters, "metal-poor" gas clouds collapse into stars, chemical enrichment occurs through stellar evolution, successor clouds collapse into stars with more "metal", and so on; black holes form, merge, and grow. All of this can be time-oriented such that the future having more entropy.
There are other "decays" of matter that can serve to break microscopic time-reversal symmetry which have been proposed and even to some extent demonstrated. Practically all of them rely on a sizable collection of in-principle reversible microscopic changes that in practice -- and in large numbers -- will not reverse. Consequently you can examine such a clock and tell if it is ticking forwards or backwards. Again, that's what's meant by time as an emergent property.